On this page of SOMA Guide you'll find a walkthrough for Phi Station and Ark location.
When the hatch opens, go straight ahead, until you reach a new room. Stick the Omnitool into the socked on the left side to restore the power to the station. When the power is back, go to the room with the "Loading Docks" sign above the doors, and climb down the ladder.
When you enter the room, go straight ahead and then take a turn to the left, into a small room - in front of the entrance there's a Battery Pack. Pick it up, turn around, head left and travel by sticking to the left wall, until you reach a room with the growth (WAU), where you can heal if Simon was injured.
To the right of WAU there's a panel - approach it and insert the freshly acquired battery in it. Get into the room, collect the ARK, and then head to the room located to the right of the ladder, by which you've entered this room.
Place the ARK into something that resembles a bullet nest, and then turn around and perform a Data Buffer on the corpse lying on the ground. Get back to the panel with the Battery Pack, pick it up and go back to the ARK - right next to the corpse on which you've performed the Data Buffer there's a control panel, which requires the battery.
Turn around, climb up the stairs and activate the panel to close the ARK chamber. Go back upstairs, pick up the Omnitool and go to the room marked as "Launch Dome", which can be found to the right of the Omnitool socket. Get inside, use the tool to close the hatch behind you and continue on.
Go outside and take a turn to the "first right", after which you have climb up the ramp. Place the Omnitool in the socket and take a seat. You now have to complete the last puzzle in the game - you must transfer the ARK to the launcher. Wait for the system to start and back to work.
You must maneuver the crane properly. Aim the orange "X" so that it is positioned directly above the bullet containing the ARK - the X will change the color to green. Press the interaction button, and when the crane picks up the ARK transport it back to the launcher, finalizing everything by pressing the interaction button again. The bullet will be loaded into the launcher. Wait until Catherine finishes talking and press the "Launch" button to fire the rocket.
Wait for the ending credits (do not turn off the game!) to end, to see how exactly the ARK looks like. When Simon wakes up, get back from the armchair and leave the cave. Go straight ahead until you reach a terminal with a survey - complete it if you want, and then continue your journey. You should soon reach Catherine, this time in a human form, which will end the game.